Ph.D.
students need a total of 72 credits beyond the B.S. or 54
credits
beyond the Master's degree. They must fulfill the following
requirements:

Pass two qualifying
exams, usually
one by the fifth term and one by the seventh: see here
for details.

Pass four 2-course
core sequences,
in real analysis (course numbers 5310-20), complex analysis (5410-20),
algebra (5520-30), and topology (5610-20).
Students passing a qualifying exam in a core area before taking the
sequence in that area may omit that sequence.

Pass six 6000 level
seminars, two
each in the areas of algebra (6310, 6510), analysis (6110/50, 6200,
6700, and 6810), and topology (6010, 6610). These courses may usually
be repeated for credit.

Take at least 9
credits of 6950,
doctoral dissertation. At most 12 credits of 6950 can count towards the
degree. Either 3, 6, or 9 credits of 6950 can be taken in any given
term, although ordinarily, at most 6 credits of reading and/or
dissertation courses should be taken in any given term. Once 6950 is
begun, it must take it every term until the Ph.D. is completed.

Defend the Ph.D.
dissertation.

M.S.
students need a total of 36 credits beyond the B.S. They
must
fulfill the following requirements:

Write a thesis and
take 6 credits of
5950, Master's dissertation. Either 3 or 6 credits of 5950 can be taken
in any given term. Once 5950 is begun, it must take it every term until
the M.A. is completed.

Only
one of 5400, 5500, and 5600 can count as credit towards any of the
three graduate degrees. Students may have at most one grade
of "C" and no grades of "D" or "F" on their degree plans for any of the
three graduate degrees.